Kesirli Cique kollokasyon metodu ile uzay kesirli Schrodinger denkleminin sayısal çözümü

Yıl 2025, Cilt: 18 Sayı: 2, 54 - 59, 26.12.2025

Mine Aylin Bayrak , Ali Demir

https://doi.org/10.58688/kujs.1702711

Öz

Bu çalışma, Uzay Kesirli Schrödinger Problemi'nin (UKSP), Kesirli Clique Kolokasyon Yöntemi (KCKM) ile sayısal çözümünün elde edilmesini konu almaktadır. Yöntem, ilk aşamada problemi, kesirli Clique polinomları temelinde kolokasyon noktaları kullanılarak bir adi diferansiyel ve cebirsel denklem sistemine dönüştürmekte; ikinci aşamada ise bu sistem Rezidüel Kuvvet Serileri Yöntemi (RKSY) ile çözülmektedir. Böylece KCKM, iki sayısal tekniğin birleşiminden oluşan hibrit bir yaklaşımdır. Yöntemin etkinliği ve üstünlüğü, sunulan nümerik örnekler üzerinden tartışılmıştır.

Anahtar Kelimeler

Uzay kesirli Schrodinger denklemi , Cilque polinomları , Rezidüel kuvvet serisi yöntemi

Numerical Solution of Space Fractional Schrodinger equation by fractional Clique collocation method

Öz

This research presents the establishment of numerical solutions for space fractional Schrodinger problem (SFSP) by utilizing significant collocation methods, called fractional Clique collocation method (FCCM). First of all, the SFSP is reduced into a system of ordinary differential and algebraic equations by means of fractional Clique polynomials with collocation points. Secondly, the resulting system is solved numerically by Residual power series method (RPSM).Therefore, FCCM is a combination of fractional Clique polynomials and RPSM. Finally, illustrative examples are given to present how FCCM is striking and appealing.

Anahtar Kelimeler

Space fractional Schrodinger equation , Clique polynomials , Residual power series method

Kaynakça

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